We study the effects of Fermi-liquid interactions on quasi-two-dimensional
d-wave superconductors in a magnetic field. The phase diagram of the
superconducting state, including the periodic Fulde-Ferrell-Larkin-Ovchinnikov
(FFLO) state in high magnetic fields, is discussed for different strengths of
quasiparticle many-body interactions within Landau's theory of Fermi liquids.
Decreasing the Fermi-liquid parameter F0a​ causes the magnetic spin
susceptibility to increase, which in turn leads to a reduction of the FFLO
phase. It is shown that a negative F0a​ results in a first-order phase
transition from the normal to the uniform superconducting state in a finite
temperature interval. Finally, we discuss the thermodynamic implications of a
first-order phase transition for CeCoIn5​.Comment: published version; removed direct comparison with experiment for the
upper critical field, as required by the referee